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A302753
Prime-additive numbers: numbers n with at least 2 distinct prime factors, that can be represented as n = Sum_{p|n} p^e_p, with e_p > 0.
3
30, 42, 60, 70, 84, 90, 102, 132, 140, 150, 170, 174, 180, 186, 228, 252, 270, 290, 294, 300, 306, 318, 350, 364, 378, 396, 442, 540, 588, 618, 650, 730, 750, 774, 804, 882, 894, 900, 906, 915, 980, 986, 1015, 1116, 1182, 1314, 1364, 1804, 1892, 1935, 2058
OFFSET
1,1
LINKS
Paul Erdős and Norbert Hegyvári, On prime-additive numbers, Studia Scientiarum Mathematicarum Hungarica, Vol. 27, No. 1-2 (1992), pp. 207-212. Review.
EXAMPLE
30 = 2 * 3 * 5 = 2 + 3 + 5^2.
42 = 2 * 3 * 7 = 2^3 + 3^3 + 7 = 2^5 + 3 + 7.
MATHEMATICA
primes[n_] := First[Transpose[FactorInteger[n]]]; maxPower[p_, n_] := Module[{k=0, nn=n}, While[nn>1, nn/=p; k++]; k-1]; a[n_] := Module[ {ps=primes[n]}, np=Length[ps]; pws=Table[maxPower[ps[[k]], n], {k, 1, np}]; npws=Length[pws]; Coefficient[Product[Sum[x^(ps[[k]]^j), {j, 1, pws[[k]]}], {k, 1, np}], x, n]]; s={}; Do[b=a[n]; If[b>0, AppendTo[s, n]], {n, 1, 2100}]; s
CROSSREFS
Sequence in context: A376862 A175727 A296717 * A179945 A136152 A244066
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 12 2018
STATUS
approved